axfr={{"AB""BA","BBA""BAAB"},{"BBA""ABAA","ABA""BAB"},{"BBBB""B","ABA""BAAB"},{"BBA""AB","AA""BABA"},{"ABA""BAAB","BBBB""B"},{"AAB""ABBB","BAB""BAAA"},{"AAA""ABAB","BA""AB","BBB""BAAB"},{"AB""BA","AA""BABA","BBB""AB"},{"BBBB""BBBA","AAAB""A","ABA""BAAB"},{"BBB""ABBA","AA""BAB","BA""AB"},{"BBBB""AA","ABA""BAAB"},{"BBA""ABA","AA""BAB"}};
MapIndexed[Show[LabelWrapper[GraphicsRow[{SMWXGraphicsStreamed[SMWEvolveListX[#,"ABAAB",20]],SMWXGraphicsStreamed[SMWEvolveListX[#,"ABAAB",20,Backward]]}],BigFont[First[#2]]]]&,axfr];
OverlapFreeQ Overlaps RuleOverlapQ SMWOverlapTest